# On the Regret of H∞ Control

arXiv: https://arxiv.org/abs/2203.16237 · HTML: https://mlsanity.com/paper/2203.16237/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Mar 2022.

## Built on by (most cited first, 5 of 5)

- [Implications of Regret on Stability of Linear Dynamical Systems](https://mlsanity.com/paper/2211.07411/) (2022)
- [Adaptive Online Non-stochastic Control](https://mlsanity.com/paper/2310.02261/) (2023)
- [Optimistic Online Non-stochastic Control via FTRL](https://mlsanity.com/paper/2404.03309/) (2024)
- [Optimal Competitive-Ratio Control](https://mlsanity.com/paper/2206.01782/) (2022)
- [Online Convex Optimization and Integral Quadratic Constraints: An automated approach to regret analysis](https://mlsanity.com/paper/2503.23600/) (2025)

## Abstract (arXiv)

The H∞ synthesis approach is a cornerstone robust control design technique, but is known to be conservative in some cases. The objective of this paper is to quantify the additional cost the controller incurs planning for the worst-case scenario, by adopting an approach inspired by regret from online learning. We define the textitdisturbance-reality gap as the difference between the predicted worst-case disturbance signal and the actual realization. The regret is shown to scale with the norm of this textitgap, which turns out to have a similar structure to that of the certainty equivalent controller with inaccurate predictions, obtained here in terms of the textitprediction error norm.